IDEAS home Printed from https://ideas.repec.org/p/hhs/oruesi/2021_005.html

Objective Bayesian meta-analysis based on generalized multivariate random effects model

Author

Listed:

Abstract

Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data-generating model, independently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated.

Suggested Citation

  • Bodnar, Olha & Bodnar, Taras, 2021. "Objective Bayesian meta-analysis based on generalized multivariate random effects model," Working Papers 2021:5, Örebro University, School of Business.
    • Handle: RePEc:hhs:oruesi:2021_005
    as

    Download full text from publisher

    File URL: https://www.oru.se/globalassets/oru-sv/institutioner/hh/workingpapers/workingpapers2021/wp-5-2021.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andrew L. Rukhin, 2013. "Estimating heterogeneity variance in meta-analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 451-469, June.
    2. Dungang Liu & Regina Y. Liu & Minge Xie, 2015. "Multivariate Meta-Analysis of Heterogeneous Studies Using Only Summary Statistics: Efficiency and Robustness," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 326-340, March.
    3. Andrew L. Rukhin, 2017. "Estimation of the common mean from heterogeneous normal observations with unknown variances," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1601-1618, November.
    4. Sutradhar, Brajendra C. & Ali, Mir M., 1989. "A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 155-162, April.
    5. Han Chen & Alisa K. Manning & Josée Dupuis, 2012. "A Method of Moments Estimator for Random Effect Multivariate Meta-Analysis," Biometrics, The International Biometric Society, vol. 68(4), pages 1278-1284, December.
    6. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
    7. William E. Strawderman & Andrew L. Rukhin, 2010. "Simultaneous estimation and reduction of nonconformity in interlaboratory studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 219-234, March.
    8. Haben Michael & Suzanne Thornton & Minge Xie & Lu Tian, 2019. "Exact inference on the random‐effects model for meta‐analyses with few studies," Biometrics, The International Biometric Society, vol. 75(2), pages 485-493, June.
    9. A. E. Ades & G. Lu & J. P. T. Higgins, 2005. "The Interpretation of Random-Effects Meta-Analysis in Decision Models," Medical Decision Making, , vol. 25(6), pages 646-654, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bodnar, Olha & Bodnar, Taras, 2024. "Gibbs sampler approach for objective Bayesian inference in elliptical multivariate meta-analysis random effects model," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    2. Bodnar, Olha & Bodnar, Taras, 2025. "Birge ratio method for modeling dark uncertainty in multivariate meta-analyses and inter-laboratory studies," Journal of Multivariate Analysis, Elsevier, vol. 205(C).
    3. Bodnar, Olha & Eriksson, Viktor, 2021. "Bayesian model selection: Application to adjustment of fundamental physical constants," Working Papers 2021:7, Örebro University, School of Business.
    4. Elena Kulinskaya & Stephan Morgenthaler & Robert G. Staudte, 2014. "Combining Statistical Evidence," International Statistical Review, International Statistical Institute, vol. 82(2), pages 214-242, August.
    5. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    6. Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2024. "Cluster GARCH," Papers 2406.06860, arXiv.org.
    7. Rongzhong Xu & Liubing Lin & Yong Li & Yan Li, 2017. "ShenQi FuZheng Injection combined with chemotherapy in the treatment of colorectal cancer: A meta-analysis," PLOS ONE, Public Library of Science, vol. 12(9), pages 1-13, September.
    8. Haas, Markus & Mittnik, Stefan, 2008. "Multivariate regimeswitching GARCH with an application to international stock markets," CFS Working Paper Series 2008/08, Center for Financial Studies (CFS).
    9. D. Stephen G. Pollock, 2021. "Multidimensional Arrays, Indices and Kronecker Products," Econometrics, MDPI, vol. 9(2), pages 1-15, April.
    10. Kang, Chul & Kim, Byung-Chun, 1996. "The N-th moment of matrix quadratic form," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 291-297, August.
    11. Ito, Tsubasa & Sugasawa, Shonosuke, 2021. "Improved confidence regions in meta-analysis of diagnostic test accuracy," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    12. Ogasawara, Haruhiko, 2023. "The density of the sample correlations under elliptical symmetry with or without the truncated variance-ratio," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    13. St'ephane Bonhomme & Koen Jochmans & Martin Weidner, 2024. "A Neyman-Orthogonalization Approach to the Incidental Parameter Problem," Papers 2412.10304, arXiv.org, revised Jan 2025.
    14. D.A. Turkington, 1997. "Some results in matrix calculus and an example of their application to econometrics," Economics Discussion / Working Papers 97-07, The University of Western Australia, Department of Economics.
    15. Shoichi Eguchi & Hiroki Masuda, 2024. "Gaussian quasi-information criteria for ergodic Lévy driven SDE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 111-157, February.
    16. Javed, Farrukh & Loperfido, Nicola & Mazur, Stepan, 2024. "Edgeworth expansions for multivariate random sums," Econometrics and Statistics, Elsevier, vol. 31(C), pages 66-80.
    17. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    18. Rezaei, Amir & Yousefzadeh, Fatemeh & Arellano-Valle, Reinaldo B., 2020. "Scale and shape mixtures of matrix variate extended skew normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    19. Jochmans, Koen, 2024. "Nonparametric identification and estimation of stochastic block models from many small networks," Journal of Econometrics, Elsevier, vol. 242(2).
    20. Sun, Yixiao, 2011. "Robust trend inference with series variance estimator and testing-optimal smoothing parameter," Journal of Econometrics, Elsevier, vol. 164(2), pages 345-366, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:oruesi:2021_005. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/ieoruse.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.